Prime knots with arc index 12 up to 16 crossings

TL;DR

This paper extends the classification of prime knots by providing a comprehensive list of prime knots with arc index 12 up to 16 crossings, including their minimal grid diagrams, significantly expanding the known catalog.

Contribution

It presents the first complete enumeration of prime knots with arc index 12 up to 16 crossings and their minimal grid diagrams, building upon previous work for lower arc indices.

Findings

Identified 19,513 prime knots with arc index 12 up to 16 crossings.

Provided minimal grid diagrams for all listed knots.

Extended the catalog of prime knots to higher arc indices.

Abstract

As a continuation of the previous works to tabulate the prime knots up to arc index 11, we provide the list of prime knots with arc index 12 up to 16 crossings and their minimal grid diagrams. There are 19,513 prime knots of arc index 12 up to 16 crossings.